Proceedings of the fourth annual ACM symposium on Theory of computing最新文献

Subrecursive program schemata I & II(I. Undecidable equivalence problems, II. Decidable equivalence problems) 子递归程序模式I & II不可判定等价问题，2。可判定等价问题)

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804892

R. Constable, S. S. Muchnick

{"title":"Subrecursive program schemata I & II(I. Undecidable equivalence problems, II. Decidable equivalence problems)","authors":"R. Constable, S. S. Muchnick","doi":"10.1145/800152.804892","DOIUrl":"https://doi.org/10.1145/800152.804892","url":null,"abstract":"The study of program schemata and the study of subrecursive programming languages are both concerned with limiting program structure in order to permit a more complete analysis of algorithms while retaining sufficiently rich computing power to allow interesting algorithms. In this paper we combine these approaches by defining classes of subrecursive program schemata and investigating their equivalence problems. Since the languages are all subrecursive, any scheme written in any one of them must halt (as long as we assume the basic functions and predicates are all total). Hence equivalence of schemes is the first question of interest we can ask about these languages. We consider schematic versions of various subrecursive programming languages similar to the Loop language. We distinguish between Pre-Loop and Post-Loop languages on the basis of whether the exit condition in an iteration loop is tested before iteration, as in Algol (Pre-), or after iteration, as in FORTRAN (Post-). We show that at the program level all these languages have the same computing power (the primitive recursive functions) and all have unsolvable equivalence problems (of arithmetic degree &pgr;01). But at the level of schemes, Pre-Loop has an unsolvable equivalence problem, while at least one formulation of Post-Loop has a solvable equivalence problem.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121664374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Linear time bounds for median computations 中位数计算的线性时间界限

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804904

M. Blum, R. W. Floyd, V. Pratt, R. Rivest, R. Tarjan

引用次数: 53

Compositions of n tree transducers n树换能器的组成

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804915

W. Ogden, W. Rounds

{"title":"Compositions of n tree transducers","authors":"W. Ogden, W. Rounds","doi":"10.1145/800152.804915","DOIUrl":"https://doi.org/10.1145/800152.804915","url":null,"abstract":"Top-down tree transductions, introduced as models of syntax-directed translations and transformational grammars in [12] and [11], are not closed under relational composition. However, closure under relational composition is not always needed; for example, in establishing closure properties of surface sets.(Surface sets are tree-languages obtained as ranges of transductions.) One such closure property, whether the image of a surface set under a transduction is a surface set, remained open. In this paper, we show that transductions need not preserve surface sets. In fact, we exhibit a hierarchy of tree languages obtained by successive transductions. We do not have a good proof that the hierarchy inclusions are proper, but there are strong reasons for so suspecting. As is customary in tree automata papers, we spend some effort on notation. This time, we present a list of first-order axioms for plane (ordered) trees. The Gorn-Brainerd-Doner representation of trees as prefix-closed sets of sequences ([5],[2],[3]) really is a representation in the sense that any (well-founded) abstract tree satisfying our axioms is isomorphic to a prefix-closed set. We then adopt Rosen's notation [10] for trees in subsequent definitions. In our opinion, however, a universally acceptable notation remains to be discovered.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116841830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

The computation of finite functions 有限函数的计算

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804911

D. Symes

引用次数: 2

Flow graph reducibility 流图可约性

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804919

M. Hecht, J. Ullman

引用次数: 185

A bound on the multiplication efficiency of iteration 迭代的乘法效率的一个界限

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804902

H. T. Kung

引用次数: 11

Algorithms for rational function arithmetic operations 有理函数算术运算的算法

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804903

E. Horowitz

引用次数: 9

Turing machines and the spectra of first-order formulas with equality 图灵机与一阶等式的谱

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804909

N. Jones, A. Selman

引用次数: 123

Binary search trees of bounded balance 有界平衡的二叉搜索树

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804906

J. Nievergelt, E. Reingold

引用次数: 303

A technique for speeding up LR(k) parsers 一种加速LR(k)解析器的技术

Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804920

A. Aho, J. Ullman

引用次数: 35